# Bond length, angle and energy

Bond length, Bond angle and Bond energy

Since atoms in a molecule are always vibrating with respect to each other, hence the question of any fixed distance between the nuclei of the atoms does not arise. Even then the average distance between the two nuclei of two bonded atoms is called bond length.

In a covalent molecule of the same atoms, bond length is double the covalent radius of the atom. While in the case of ionic compounds, bond length is sum of the ionic radii of cation and anion. Bond lengths of some common diatomic molecules are given in the following table.

It is clear from the table that multiple bonds are shorter than a single bond, bond length increases with the increase of involvement of p-orbit. C – H bond distance $(\AA)$ in $sp, sp^2 \text{and} sp^2$ hybridized molecule is 1.057 1.087 and 1.093 $\AA$ respectively.

Bond Length $(\AA)$ of some common covalent bonds

1. Bond: H – H , Bond length: 0.751
2. Bond: F – F, Bong length: 1.435
3. Bond: Cl – Cl, Bond length: 2.002
4. Bond: Br – Br, Bond length: 2.286
5. Bond: Cl – Cl, Bond length: 2.002
6. Bond: I – I, Bond length: 21.470
7. Bond: $N \equiv N$, Bond length: 1.094
8. Bond: H – F, Bond length: 0.926
9. Bond: H – Cl, Bond length: 1.284
10. Bond: H – Br, Bond length: 1.423
11. Bond: H – I, Bond length: 1.615
12. Bond: H – O, Bond length: 0.957
13. Bond: H – S, Bond length: 1.334
14. Bond: H – N, Bond length: 1.014
15. Bond: C – C, Bond length: 1.543
16. Bond: C = C, Bond length: 1.330
17. Bond: $C \equiv C$, Bond length: 1.200
18. Bond: O – O, Bond length: 1.480
19. Bond O = O, Bond length: 1.207
20. Bond C – O, Bond length: 1.420
21. Bond C = O, Bond length: 1.220

It is important to note that the values given in the above table do not, hold good for all compounds. Because bond length is not a simple addition of the ionic or covalent radii of the two concerned atoms. There are several factors which are responsible for bond length such as resonance, hybridization, electronegativity and steric effect.

$\text{Bond Length} \propto \dfrac{1}{\text{Electronegativity difference}} \\[3mm] \propto e^- - e^- \text{Repulsion} \\[3mm] \propto \dfrac{1}{\text{Bond order}} \\[3mm] \propto \dfrac{1}{s \%} \\ (sp^3 > sp^2 > sp)$
• Resonance changes bond length e.g. in benzene [C – C is 1.39 $\AA$ ].
• Hyper conjugation also changes bond length as in Buta 1. 2 di-ene.

Bond angle is the internal angle between the orbitals having bonded pair of electrons in the valency shell of the central atom in a molecule e.g. the bond angel in $H_2O, NH_3 \text{and} CH_4 \text{is} 105.5^0, 107.8^0 \text{and} 109.5^0$, respectively.

Bond angel depends upon type of hybridization, presence of lone pair of electrons and electronegativity of the atom.

$\text{Bond angle} \propto \text{Electronegativity difference} \\ \propto \text{Bond order} \\ \propto s \% \\ \propto \text{size of terminal atom} \\ eq: I_2O > Br_2O > Cl_2O > OF_2$.

Bond energy or strength is the amount of energy required to break one mole of chemical bond in a gaseous state. The bond energies of some of the diatomic molecules are given as follows:

Bond energies $(Kj mol^{-1})$ of some common covalent bonds

 Bond Bond Energy Bond Bond Energy Bond Bond Energy C –C 347.3 N – N 163.2 C-N 285.0 C = C 606.7 N = N 418.5 C = N 615.1 C $\equiv$ C 803.3 N $\equiv$ N 945.6 C$\equiv$ N 666.1 C – O 309.6 N – O 200.8 O – O 146.4 C = O 694.5 N = O 611.0 O = O 497.9 C $\equiv$ 0 1071.3 H – H 436.0 S – S 226.0 Cl -CL 242.6 P – P 200.8 Se – Se 171.5 Br – Br 193.0 As – As 146.4 H – O 462.6 I- I 150.6 H – C 415.5 H – S 347.3 H – Cl 431.0 C – Cl 327.2 H – Se 276.1

Salient features of Bond energies are as follows:

(i) It is greater for $\sigma$ bond than $\pi$ bond

(ii) It increases as the number of bond increases between the atoms, i.e.,

$C- C < C = C < C \equiv C \\ C - N < C = N < C \equiv N$

(iii) It increases with increase of the contribution of p-orbitals as $sp < sp^2 < sp^3$.

(iv) It decreases as the number of lone pairs of electrons increases.

E.g.

(v) It decreases from top to bottom in the group g.e.

Cl – Cl > Br – Br > I – I

H – H > Li – Li > Na – Na > K – K

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